# An engel condition with skew derivations

Ming Chu Chou, Cheng Kai Liu

Research output: Contribution to journalArticle

21 Citations (Scopus)

### Abstract

Let R be a prime ring and set [x, y]1 = [x, y] = xy - yx for x, y ∈ R and inductively [x, y]k = [[x, y]k-1, y] for k > 1. We apply the theory of generalized polynomial identities with automorphisms and skew derivations to obtain the following result: If δ is a nonzero σ-derivation of R and L is a noncommutative Lie ideal of R so that [δ(x), x]k = 0 for all x ∈ L, where k is a fixed positive integer, then charR = 2 and for some field F. This result generalizes the case of derivations by Lanski and also the case of automorphisms by Mayne.

Original language English 259-270 12 Monatshefte fur Mathematik 158 3 https://doi.org/10.1007/s00605-008-0043-5 Published - 2009 Jan 1

### Fingerprint

Skew Derivation
Automorphisms
Generalized Polynomial Identity
Lie Ideal
Prime Ring
Generalise
Integer

### All Science Journal Classification (ASJC) codes

• Mathematics(all)

### Cite this

Chou, Ming Chu ; Liu, Cheng Kai. / An engel condition with skew derivations. In: Monatshefte fur Mathematik. 2009 ; Vol. 158, No. 3. pp. 259-270.
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An engel condition with skew derivations. / Chou, Ming Chu; Liu, Cheng Kai.

In: Monatshefte fur Mathematik, Vol. 158, No. 3, 01.01.2009, p. 259-270.

Research output: Contribution to journalArticle

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